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- W3211659228 abstract "Let $G=(V(G),E(G))$ be a simple graph. A restrained double Roman dominating function (RDRD-function) of $G$ is a function $f: V(G) rightarrow {0,1,2,3}$ satisfying the following properties: if $f(v)=0$, then the vertex $v$ has at least two neighbours assigned 2 under $f$ or one neighbour $u$ with $f(u)=3$; and if $f(v)=1$, then the vertex $v$ must have one neighbor $u$ with $f(u) geq 2$; the induced graph by vertices assigned 0 under $f$ contains no isolated vertex. The weight of a RDRD-function $f$ is the sum $f(V)=sum_{v in V(G)} f(v)$, and the minimum weight of a RDRD-function on $G$ is the restrained double Roman domination number (RDRD-number) of $G$, denoted by $gamma_{rdR}(G)$. In this paper, we first prove that the problem of computing RDRD-number is NP-hard even for chordal graphs. And then we study the impact of some graph operations, such as strong product, cardinal product and corona with a graph, on restrained double Roman domination number." @default.
- W3211659228 created "2021-11-22" @default.
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- W3211659228 date "2023-01-01" @default.
- W3211659228 modified "2023-10-17" @default.
- W3211659228 title "The Restrained Double Roman Domination and Graph Operations" @default.
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- W3211659228 doi "https://doi.org/10.2139/ssrn.4520713" @default.
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